CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

NEW

Advanced ConstitutiveModels for Challenging Forming Simulations by Frédéric Barlat and Toshihiko Kuwabara

The results of finite element (FE) simulations involving large plastic deformation such as forming depend on a large num- ber of parameters. Beside numerical parameters, physical input such as boundary condition, contact and interface, and material behavior are playing a key role. This article deals only with the latter, more precisely, the influence of the consti- tutive description on forming simulation results. Large scale simulations performed in industry on real scale products are very challenging because of the size of the FE model. How- ever, this is not addressed in this article, which focuses on the forming simulations of laboratory scale specimens. Simulations of simple laboratory tests For instance, an accurate prediction of springback in U-draw bending for a simple rectangular blank made of advanced high strength steel is difficult to achieve. Better results are usually obtained if an advanced constitutive model is em- ployed. First, this requires the use of an elastic cord modulus that is a function of the accumulated plastic strain. Second, the plasticity model should consist of a non-quadratic aniso- tropic yield condition and an anisotropic hardening approach. The latter is necessary because of the forward-reverse load- ing occurring when the material flows through the proximity of a die corner. It is well known that strain hardening with a large transient effect occurs during non-linear loading. Of course, this type of constitutive description requires the measurement of mechanical properties in different directions and for various stress states. Moreover, it should include a few cycles in a forward-reversal mode of deformation, which requires proper equipment and operation.

compression symmetry, uniaxial tension tests are the easiest to conduct but a large number of loading directions should be considered, typically, at every 15° from rolling. Even with an advanced anisotropic yield condition, some discrepancies with experimental results are expected if hardening is as- sumed to be isotropic because the material flowing over a die radius experiences forward-reverse deformations cycles. The indentation of a pre-stretched panel requires the use of an advanced constitutive model as well because the pre-strain and indentation correspond usually to two different stress states. In addition, the variation of the elastic modulus must be characterized for a balanced biaxial stress state.

Figure 2: Schematics of FE simulations for HE test Simulation of hole expansion test

The remaining of this article focuses on the simulations of the flat hole expansion (HE) test [3]. Experiments were conducted on a high r-value, extra deep drawing quality steel (EDDQ), with the set-up represented in Fig. 1. The contact between the punch and the sheet was lubricated with Teflon and Vaseline leading to a friction coefficient μ = 0.03. A constant blank holding force of 60 kNwas applied to the blank and the experiment ended at a punch stroke of 30 mm. After this test, the specimen radial strains were measured along the rolling (RD) and transverse (TD) directions, and at 45° from the RD. Simulations were conducted with Abaqus/ standard 6.12 using 4-node shell element with reduced integration (S4R) assuming isotropic hardening with the same stress-strain curve for all the cases but different yield conditions. The isotropic VonMises, anisotropic Hill’s 48 and anisotropic Yld2000-2d yield conditions were employed with, for the latter, a characteristic exponent M. Two cases were considered, namely, M= 5.85, which was determined from best approximation of biaxial test data, andM= 6, which is the standard value for BCC materials. The constitutive model characterization and FE simulations were conducted accord- ing to the schematics of Fig. 2. Fig. 3 represents the experimental yield locus determined at a constant plastic work corresponding to an effective strain of 0.24. Fig. 3 also provides the predicted loci calculated with vonMises, Hill’s 48 identified mostly with uniaxial r-values, and Yld2000-2d withM= 5.85 and 6. This figure

Figure 1: Sketch of hole expansion (HE) test Other simple challenging simulations include cup drawing of a circular blank [1], indentation of a pre-stretched panel [2] and expansion of a circular hole [3]. In the case of cup drawing, the prediction of the earing profile, that is, the strain field in the product, requires a precise description of the material behavior in stress states that are close to those encountered in the flange of a cup. These states fluctuate between pure shear and simple compression, in which the thickness strain variation is limited. For this purpose, assuming tension

63